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The Vakhitov–Kolokolov stability criterion is a condition for linear stability of solitary wave solutions to a wide class of U-invariant Hamiltonian systems, named after Soviet scientists Aleksandr Kolokolov and Nazib Vakhitov.The condition for linear stability of a solitary wave u = ϕ ω e − i ω t {\displaystyle u=\phi _{\omega }e^{-i\omega t}} with frequency ω {\displaystyle \omega } has the form
where Q {\displaystyle Q\,} is the charge of the solitary wave ϕ ω e − i ω t {\displaystyle \phi _{\omega }e^{-i\omega t}} ,conserved by Noether's theorem due to U-invariance of the system.